This invention relates to a method of creating the curved surface of a three-dimensional body and, more particularly, to a method of creating curved surfaces that, is ideal for the preparation of a numerical control (NC) tape required for the numerically controlled machining of a three-dimensional metal mold or the like.
A curved surface of a three-dimensional metal mold or the like, when drawn out on the plane of a blueprint, is generally represented by a plurality of given section curves, but no data is shown for the shape of the area lying between a certain section curve and the next adjacent section curve. When carrying out numerically controlled machining it is essential that these two section curves be connected smoothly despite the fact that the shape of the area between them is not given. In other words, this means that machining must be performed by generating the curved surface between the two section curves from such data as that indicative of the section curves, punching an NC tape so as to incorporate the data concerning the generated curved surface, and then machining the workpiece in accordance with the instructions on the NC tape. To this end, the numerical control tape ordinarily is prepared by using a computer, and either of two methods can be adopted to create the curved surface, namely (1) a patch system in which processing is executed by partitioning a curved surface into minute portions, and (2) a system in which a two-dimensional curve made of straight line segments and arcs is modified for each pick-feed applied to a third axis.
The patch system (1), however, entails the processing of large quantities of data as well as highly complicated mathematical processing, and requires a large-scale computer system. The system (2) makes processing with a small-scale computer possible, but there is no three-dimensional tool offset capability and there is an excessive limitation upon tool movement direction and machining shape, making it impossible to create sophisticated three-dimensional bodies.
Accordingly, the inventors have already proposed a method of creating curved surfaces, comprising generating a plurality a intermediate sections and finding a section curve (intermediate section curve) on a curved body, based on the intermediate sections, in accordance with predetermined rules, from section data specifying given sections of a three-dimensional curved body and from data specifying section curves in said sections, and generating the curved surface of the three-dimensional body based on the plurality of generated intermediate section curves. In other words, with the previously proposed method, one of two given section curves is shifted, while being transformed, so as to be superposed on the second section curve, at which time the curved surface formed by shifting the first section curve is generated as a collection of a plurality of intermediate section curves. In generating the intermediate section curves, uniform correspondence is established between the first and second section curves in their entirety. More specifically, when each section curve is partitioned into M segments, correspondence is established between i-th (i=1,2, . . . n) partitioning points Pi, Qi on the respective curves. Each of the intermediate section curves is generated using this corresponding relationship.
When a single, unique corresponding relationship between section curves is decided in this manner, however, freedom in creating a curved surface is lost so that there are cases where a curved surface featuring subtle changes cannot be created with accuracy. For example, in a case where one section curve is composed of a curve segment A having little curvature and a gentle curve segment B that is much longer than the curve segment A, the curved surface near the curve segment A cannot be expressed accurately with the above-described method. In addition, the foregoing curved surface generation method is not suitable when it is desired to obtain a curved surface which is slightly different from a curved surface created based on the uniform corresponding relationship.